Anomalous diffusion for a class of systems with two conserved quantities
Résumé
We introduce a class of one-dimensional deterministic models of energy- volume conserving interfaces. Numerical simulations show that these dynamics are genuinely super-diffusive. We then modify the dynamics by adding a conservative stochastic noise so that it becomes ergodic. A system of conservation laws are derived as hydrodynamic limits of the modified dynamics. Numerical evidence shows that these models are still super-diffusive. This is proven rigorously for harmonic potentials.
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